arXiv subjects

Dylan Lewis

Publications and source records attributed to Dylan Lewis.

14 recordsLinked to original sources

arXiv2026

Self-Attention for Quantum Entanglement Prediction

Quantum entanglement is a powerful resource for quantum-enhanced technologies. However, its reliable quantification remains challenging due to the exponential scaling of the Hilbert space with system size, which renders full state tomography infeasible. Moreover, experimentally estimating entanglement typically requires a large number of measurement samples leading to a significant overhead. In this work, we present two models, a feed-forward neural network and an attention-based model, to accurately predict the bipartite second Renyi from projective measurements of quantum states. We benchmark their performance against standard classical shadow estimators and find that the machine-learning approaches achieve higher accuracy and improved sample efficiency across a range of system sizes. Our results demonstrate the potential of machine learning for scalable and efficient estimation of quantum correlations.

quant-ph↗

arXiv2026

Pulse Quality Optimisation in Quantum Optimal Control

Quantum optimal control methods are widely used to design experimental control pulses such as laser amplitudes, phases, or detunings, that implement a target unitary evolution. In practice, what makes a pulse "good" depends not only on its fidelity, but also on the experimental setting and the relevant hardware constraints. Here, we introduce geometric quantum control with kernel optimisation (GECKO), a model-agnostic method for improving control pulses after a high-fidelity solution has been found. GECKO uses the Riemannian geometry of the special unitary group to identify directions in pulse space that leave the implemented unitary unchanged to first order, allowing one to traverse level sets of the control landscape while optimising a chosen differentiable pulse-quality function. We demonstrate GECKO on a transverse-field Ising Hamiltonian implementing CZ and CNOT gates, optimising pulse properties including spectral filtering, smoothness, robustness to parameter deviations, and pulse duration. In all cases, GECKO finds substantially improved pulse solutions.

quant-ph↗

arXiv2026

Spin qubit gates via phonon buses in electron nanowires

Scalable architectures for quantum computing using semiconductor quantum dots require interactions between qubits beyond adjacent quantum dots. Here, we propose using nanowires of electrons to mediate the interaction between two quantum dots. Virtual phonons in the linear chain of electrons can mediate an interaction that gives rise to effective spin-spin coupling of the electrons in distant quantum dots. We find coupling strengths of more than 30 MHz for experimentally realisable parameters in GaAs quantum dots.

cond-mat.mes-hall↗

arXiv2025

Time-Efficient Quantum Many-Body State Synthesis and its Optimization via Warm Start Strategies

Quantum mechanical ground states of many-body systems can be important resources for various investigations: for quantum sensing, for benchmarking quantum hardware with classically solvable states, as the initial states for nonequilibrium quantum dynamics following quenches, the simulation of quantum processes that start by coupling systems in ground states, eg, could be a process in quantum chemistry, while their approximations are required as inputs to quantum phase estimation algorithm. However, preparing ground states can be challenging; for example, it may require adiabatic switching of Hamiltonian terms slower than an inverse gap, which can be time consuming and bring in decoherence. Here we investigate the possibility of preparing a many-body entangled ground state of a certain Hamiltonian, which can be called a quantum ``problem'' Hamiltonian, using the time evolution of an initial fiducial state by another time independent ``solver'' Hamiltonian with couplings up to unit strength for a very short fixed (unit) time: a ``time efficient'' ansatz. The parameters of the solver Hamiltonian are optimised classically minimising energy as the cost function. We present a study of up to $n=14$ qubit many-body states prepared using this methodology. Importantly, we find that a strategy of combining a warm start (an already prepared ground state of a $n-1$ qubit Hamiltonian) and incrementally adding extra couplings of a qubit is the best scaling strategy to prepare the ground state of a $n$-qubit Hamiltonian.

quant-ph↗

arXiv2025

Quantum Optimal Control with Geodesic Pulse Engineering

Designing multi-qubit quantum logic gates with experimental constraints is an important problem in quantum computing. Here, we develop a new quantum optimal control algorithm for finding unitary transformations with constraints on the Hamiltonian. The algorithm, geodesic pulse engineering (GEOPE), uses differential programming and geodesics on the Riemannian manifold of $\textrm{SU}(2^n)$ for $n$ qubits. We demonstrate significant improvements over the widely used gradient-based method, GRAPE, for designing multi-qubit quantum gates. Instead of a local gradient descent, the parameter updates of GEOPE are designed to follow the geodesic to the target unitary as closely as possible. We present numerical results that show that our algorithm converges significantly faster than GRAPE for a range of gates and can find solutions that are not accessible to GRAPE in a reasonable amount of time. The strength of the method is illustrtated with varied multi-qubit gates in 2D neutral Rydberg atom platforms.

quant-ph↗

arXiv2024

Quantum Carleman linearisation efficiency in nonlinear fluid dynamics

Computational fluid dynamics (CFD) is a specialised branch of fluid mechanics that utilises numerical methods and algorithms to solve and analyze fluid-flow problems. One promising avenue to enhance CFD is the use of quantum computing, which has the potential to resolve nonlinear differential equations more efficiently than classical computers. Here, we try to answer the question of which regimes of nonlinear partial differential equations (PDEs) for fluid dynamics can have an efficient quantum algorithm. We propose a connection between the numerical parameter, $R$, that guarantees efficiency in the truncation of the Carleman linearisation, and the physical parameters that describe the fluid flow. This link can be made thanks to the Kolmogorov scale, which determines the minimum size of the grid needed to properly resolve the energy cascade induced by the nonlinear term. Additionally, we introduce the formalism for vector field simulation in different spatial dimensions, providing the discretisation of the operators and the boundary conditions.

quant-ph↗

arXiv2024

Quantum spatial search with multiple excitations

Spatial search is the problem of finding a marked vertex in a graph. A continuous-time quantum walk in the single-excitation subspace of an $n$ spin system solves the problem of spatial search by finding the marked vertex in $O(\sqrt{n})$ time. Here, we investigate a natural extension of the spatial search problem, marking multiple vertices of a graph, which are still marked with local fields. We prove that a continuous-time quantum walk in the $k$-excitation subspace of $n$ spins can determine the binary string of $k$ marked vertices with an asymptotic fidelity in time $O(\sqrt{n})$, despite the size of the state space growing as $O(n^k)$. Numerically, we show that this algorithm can be implemented with interactions that decay as $1/r^\alpha$, where $r$ is the distance between spins, and an $\alpha$ that is readily available in current ion trap systems.

quant-ph↗

arXiv2024

Geodesic Algorithm for Unitary Gate Design with Time-Independent Hamiltonians

Larger multi-qubit quantum gates allow shallower, more efficient quantum circuits, which could decrease the prohibitive effect of noise on algorithms for noisy intermediate-scale quantum (NISQ) devices and fault-tolerant error correction schemes. Such multi-qubit gates can potentially be generated by time-independent Hamiltonians comprising only physical (one- and two-local) interaction terms. Here, we present an algorithm that finds the time-independent Hamiltonian for a target quantum gate on $n$ qubits by using the geodesic on the Riemannian manifold of $\mathrm{SU}(2^n)$. Differential programming is used to determine how the Hamiltonian should be updated in order to follow the geodesic to the target unitary as closely as possible. We show that our geodesic algorithm outperforms gradient descent methods for standard multi-qubit gates such as Toffoli and Fredkin. The geodesic algorithm is then used to find previously unavailable multi-qubit gates implementing high fidelity parity checks, which could be used in a wide array of quantum codes and increase the clock speed of fault-tolerant quantum computers. The geodesic algorithm is demonstrated on an example relevant to current experimental hardware, illustrating a circuit speed up.

quant-ph↗

arXiv2023

Limitations for Quantum Algorithms to Solve Turbulent and Chaotic Systems

We investigate the limitations of quantum computers for solving nonlinear dynamical systems. In particular, we tighten the worst-case bounds of the quantum Carleman linearisation (QCL) algorithm [Liu et al., PNAS 118, 2021] answering one of their open questions. We provide a further significant limitation for any quantum algorithm that aims to output a quantum state that approximates the normalized solution vector. Given a natural choice of coordinates for a dynamical system with one or more positive Lyapunov exponents and solutions that grow sub-exponentially, we prove that any such algorithm has complexity scaling at least exponentially in the integration time. As such, an efficient quantum algorithm for simulating chaotic systems or regimes is likely not possible.

quant-ph↗

arXiv2023

Low-Dissipation Data Bus via Coherent Quantum Dynamics

The transfer of information between two physical locations is an essential component of both classical and quantum computing. In quantum computing the transfer of information must be coherent to preserve quantum states and hence the quantum information. We establish a simple protocol for transferring one- and two-electron encoded logical qubits in quantum dot arrays. The theoretical energetic cost of this protocol is calculated - in particular, the cost of freezing and unfreezing tunnelling between quantum dots. Our results are compared with the energetic cost of shuttling qubits in quantum dot arrays and transferring classical information using classical information buses. Only our protocol can manage constant dissipation for any chain length. This protocol could reduce the cooling requirements and constraints on scalable architectures for quantum dot quantum computers.

quant-ph↗

arXiv2023

Here comes the SU(N): multivariate quantum gates and gradients

Variational quantum algorithms use non-convex optimization methods to find the optimal parameters for a parametrized quantum circuit in order to solve a computational problem. The choice of the circuit ansatz, which consists of parameterized gates, is crucial to the success of these algorithms. Here, we propose a gate which fully parameterizes the special unitary group $\mathrm{SU}(N)$. This gate is generated by a sum of non-commuting operators, and we provide a method for calculating its gradient on quantum hardware. In addition, we provide a theorem for the computational complexity of calculating these gradients by using results from Lie algebra theory. In doing so, we further generalize previous parameter-shift methods. We show that the proposed gate and its optimization satisfy the quantum speed limit, resulting in geodesics on the unitary group. Finally, we give numerical evidence to support the feasibility of our approach and show the advantage of our gate over a standard gate decomposition scheme. In doing so, we show that not only the expressibility of an ansatz matters, but also how it's explicitly parameterized.

quant-ph↗

arXiv2022

Variational Quantum Circuits for Multi-Qubit Gate Automata

Implementing quantum operations in the form of natural Hamiltonian dynamics is desirable, since they almost require no external control or feedback. In this work, we propose a NISQ-friendly quantum-classical hybrid approach to designing a time-independent Hamiltonian that generates a given multi-qubit unitary. In particular, we execute a Variational Quantum Algorithm, whose ansatz is carefully chosen to be a sequence of appropriately parametrized unitaries describing at most two-qubit nearest neighbour interactions, dictating the target unitary. Subsequently, we apply our approach to simulate multi-qubit target gates, with and without stochastic noise. We demonstrate that our strategy allows us to implement a Toffoli gate with sufficiently high fidelity, as compared to the other similar techniques. Our approach is an example of the usage of quantum computing for the design of quantum computers.

quant-ph↗

arXiv2022

Ion Trap Long-Range XY Model for Quantum State Transfer and Optimal Spatial Search

Linear ion trap chains are a promising platform for quantum computation and simulation. The XY model with long-range interactions can be implemented with a single side-band Molmer-Sorensen scheme, giving interactions that decay as $1/r^\alpha$, where $\alpha$ parameterises the interaction range. Lower $\alpha$ leads to longer range interactions, allowing faster long-range gate operations for quantum computing. However, decreasing $\alpha$ causes an increased generation of coherent phonons and appears to dephase the effective XY interaction model. We characterise and show how to correct for this effect completely, allowing lower $\alpha$ interactions to be coherently implemented. Ion trap chains are thus shown to be a viable platform for spatial quantum search in optimal $O(\sqrt{N})$ time, for $N$ ions. Finally, we introduce a $O(\sqrt{N})$ quantum state transfer protocol, with a qubit encoding that maintains a high fidelity.

quant-ph↗

arXiv2020

Optimal quantum spatial search with one-dimensional long-range interactions

Continuous-time quantum walks can be used to solve the spatial search problem, which is an essential component for many quantum algorithms that run quadratically faster than their classical counterpart, in $\mathcal O(\sqrt n)$ time for $n$ entries. However the capability of models found in nature is largely unexplored - e.g., in one dimension only nearest-neighbour Hamiltonians have been considered so far, for which the quadratic speedup does not exist. Here, we prove that optimal spatial search, namely with $\mathcal O(\sqrt n)$ run time and large fidelity, is possible in one-dimensional spin chains with long-range interactions that decay as $1/r^\alpha$ with distance $r$. In particular, near unit fidelity is achieved for $\alpha\approx 1$ and, in the limit $n\to\infty$, we find a continuous transition from a region where optimal spatial search does exist ($\alpha<1.5$) to where it does not ($\alpha>1.5$). Numerically, we show that spatial search is robust to dephasing noise and that, for realistic conditions, $\alpha \lesssim 1.2$ should be sufficient to demonstrate optimal spatial search experimentally with near unit fidelity.

quant-ph↗